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Many moons ago when my son first watched DiCaprio and Winslet he queried about how the lights on the Titanic managed to stay on for so long before the ship finally sank. The electricity generators consumed something like nearly a quarter of the output power from the engines when all lights were switched on. How long could the engines supply the generators with enough power for the lights without being supplied with coal? The engine compartments flooded after the Titanic hit the iceberg so many of the engines would have been put out of action shortly afterwards. Salt water entered the electrical systems as the Titanic sank creating short circuits which would have caused fuses to blow thereby extinguishing lighting for large sections all in one go.

Did the lights gradually dim as the Titanic sank as the engines lost power or did they tend to switch off suddenly as fuses blew? At what time did the lights finally go out?

I would guess that a lot of the lights were DC with a central battery, so would keep going until the fuses blew.
William Moyes was recognised as sacrificing himself in order to keep the lights on. There is a memorial to him in his native Stirling.

The Titanic mains supply was 100V DC. Presumably this was somewhat standardised either for use on land or at sea in 1912 in order to warrant the mass production of incandescent bulbs, motors, and heating elements used on the Titanic. Did many other White Star Line and Cunard passenger ships also use 100V DC mains supplies? The electricity on the Titanic was generated by four 400kW generators located deep down in the depths of the Tank Top deck below the Orlop deck, complimented by two 30kW generators located above the turbine room which supplied power for emergency lighting. The generators were located close to the stern so were not flooded out as the Titanic sank although the boiler rooms which powered them were. The use of emergency lighting did not feature in DiCaprio and Winslet.

I suspect that all or most of the lights would have gone out fairly early in the disaster.
The provision of two smaller emergency generators suggests that no central battery emergency lighting was installed.

Although these emergency generators were not flooded, I would presume that the steam supply to them would have failed very early, as the boiler rooms were flooded.

Films are seldom acurate in such respects.
After all, if the lights in the film went out early in the disaster, there would not be much to see !.
Persons fleeing in complete darkness and attempting to board lifeboats in darkness, and then drowning in the dark would not make much of a film.

Electric lighting was a fairly new invention then, and I expect that oil lanterns were kept in reserve in key places, but the light from an actual or simulated oil lantern would not make much of a picture.

Nice query. I didn't notice that because I'm so much involved to the scene. Well in some film there are times that they did not base on the reality. Like what happen in the movie the lights are still there even though it is sinking.